{
  "translations": {
    "en": {
      "sc1": "We first examine the worst case cost.",
      "sc2": "The body of inssort contains two nested for loops.",
      "sc3": "The outer for loop is executed $n-1$ times.",
      "sc4": "The inner loop is harder to analyze since it depends on how many records in positions $0$ to $i-1$ have a value less than that of the record in position $i$.",
      "sc5": "Let's consider now a worst case example of an array with 6 elements. Since it is the worst case, each iteration of the outer loop does the greatest possible number of comparisons.",
      "sc6": "At $i=1$ a single comparison is required. We draw one box.",
      "sc7": "At $i=2$ two comparisons are required. We draw two boxes.",
      "sc9": "At $i=3$ three comparisons are required, so three boxes.",
      "sc12": "At $i=4$ four comparisons are required, so four boxes.",
      "sc16": "At $i=5$ five comparisons are required, so five boxes.",
      "sc21": "The total running time now will be the total surface area of this shape.",
      "sc22_1": "The total area will be the sum of the areas of the big triangle <br>",
      "sc22_2": "+ <br> the series of $(n-1)$ small triangles.",
      "sc23": "<br>So, the total area is $\\frac{(n-1)(n-1)}{2} + \\frac{(n-1)}{2}$ which gives $\\frac{n(n-1)}{2}$.",
      "sc24": "Therefore, the worst case running time of insertion sort is $\\theta(n^2)$."
    }
  },
  "code": {
    "java_generic": [{
      "url": "../../../SourceCode/Java_Generic/Sorting/Insertionsort.java",
      "lineNumbers": false,
      "startAfter": "/* *** ODSATag: Insertionsort *** */",
      "endBefore": "/* *** ODSAendTag: Insertionsort *** */",
      "tags": {
        "loops": [2, 3],
        "loop1": 2,
        "loop2": 3
      }
    }],
    "c++": [{
      "url": "../../../SourceCode/C++/Sorting/Insertionsort.cpp",
      "lineNumbers": false,
      "startAfter": "/* *** ODSATag: Insertionsort *** */",
      "endBefore": "/* *** ODSAendTag: Insertionsort *** */",
      "tags": {
        "loops": [2, 3],
        "loop1": 2,
        "loop2": 3
      }
    }],
    "java": [{
      "url": "../../../SourceCode/Java/Sorting/Insertionsort.java",
      "lineNumbers": false,
      "startAfter": "/* *** ODSATag: Insertionsort *** */",
      "endBefore": "/* *** ODSAendTag: Insertionsort *** */",
      "tags": {
        "loops": [2, 3],
        "loop1": 2,
        "loop2": 3
      }
    }],
    "python": [{
      "url": "../../../SourceCode/Python/Sorting/Insertionsort.py",
      "startAfter": "/* *** ODSATag: Insertionsort *** */",
      "endBefore": "/* *** ODSAendTag: Insertionsort *** */",
      "tags": {
        "sig": 1,
        "outloop": 2,
        "inloop": 4,
        "swap": 5,
        "end": 6
      }
    }]
  }
}